We analyze the characteristic features of jam formation on a circular
one-lane road. We have applied an optimal velocity model including stochastic noise, where cars are treated as moving and interacting particles. The motion of N cars is described by the system of 2N stochastic differential equations with multiplicative white noise. Our system of cars behaves in qualitatively different ways depending on the values of control parameters c (dimensionless density), b (sensitivity parameter characterising the fastness of relaxation), and α (dimensionless noise intensity). In analogy to the gas-liquid phase transition in supersaturated vapour at low enough temperatures, we observe three different regimes of traffic flow at small enough values of b < bcr. There is the free flow regime (like gaseous phase) at small densities of cars, the coexistence of a jam and free flow (like liquid and gas) at
intermediate densities, and homogeneous dense traffic (like liquid phase) at large densities. The transition from free flow to congested traffic occurs when the homogeneous solution becomes unstable and evolves into the limit cycle. The opposite process takes place at a different density, so that we have a hysteresis effect and phase transition of the first order. A phase transition of second order, characterised by critical exponents, takes place at a certain critical density c = ccr.
Inclusion of the stochastic noise allows us to calculate the distribution of headway distances and time headways between the successive cars, as well as the distribution of jam (car cluster) sizes in a congested traffic.
We present a comparison of nucleation in an isothermal-isochoric container with traffic congestion on a one-lane freeway. The analysis is based, in both cases, on the probabilistic description by stochastic master equations. Further we analyze the characteristic features of traffic breakdowns. To describe this phenomenon we apply the stochastic model regarding the jam emergence to the formation of a large car cluster on the highway.
We present preliminary experimental data that enable us to suggest that heat transfer in cellular tissue under local strong heating is a more complex phenomenon than a simple heat diffusion. Namely, we demonstrate that under local strong heating of a muscle tissue heat transfer in it exhibits substantial anisotropy unexplained in the context of the standard diffusion model. The observed temperature dynamics is also characterized by nonlinear behavior as well as by a certain repeat reversibility. The latter means that the time variations in the temperature of a cellular tissue undergoing repeated acts of heating go in the same way at least approximately. We explain the observed anomalous properties of heat transfer by suggesting the flow of the interstitial liquid to appear due to nonuniform heating which, in turn, affects the heat transfer. A possible mechanism responsible for this effect is discussed.
We analyze the necrosis growth due to thermal coagulation induced by laser light absorption and limited by heat diffusion into the surrounding live tissue. The tissue is assumed to contain a certain tumor in the undamaged tissue whereof the blood perfusion rate does not change during the action. By contrast, the normal tissue responds strongly to increase in the tissue temperature and the blood perfusion rate can grow by tenfold. We study in detail the necrosis formation under conditions typical for a real course of thermal therapy treatment, the duration of the action is taken about 5 minutes when a necrosis domain of size about or above 1 cm is formed. In particular, if the tumor size is sufficiently large, it is about 1 cm, and the tissue response is not too delayed, the delay time does not exceed 1 min, then there are conditions under which the relative volume of the damaged normal tissue is small in comparison with the tumor volume after the tumor is coagulated totally.
Previously we have developed a free boundary model for local thermal coagulation induced by laser light absorption when the tissue region affected directly by laser light is sufficiently small and heat diffusion into the surrounding tissue governs the necrosis growth. In the present paper keeping in mind the obtained results we state the point of view on the necrosis formation under these conditions as the basis of an individual laser therapy mode exhibiting specific properties. In particular, roughly speaking, the size of the resulting necrosis domain is determined by the physical characteristics of the tissue and its response to local heating, and by the applicator form rather than the treatment duration and the irradiation power.
Previously we have developed a free boundary model for local thermal coagulation induced by laser light absorption when the tissue region affected directly by laser light is sufficiently small and heat diffusion into the surrounding tissue governs the necrosis growth. In the present paper keeping in mind the obtained results we state the point of view on the necrosis formation under these conditions as the basis of an individual layer therapy mode exhibiting specific properties. In particular, roughly speaking, the size of the resulting necrosis domain is determined by the physical characteristics of the tissue and its response to local heating, and by the applicator form rather than the treatment duration and the irradiation power.
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